{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:R7RRFSJQF2B5PU5MRXBVVIBSCV","short_pith_number":"pith:R7RRFSJQ","schema_version":"1.0","canonical_sha256":"8fe312c9302e83d7d3ac8dc35aa0321557342400f6f7b1f52306179cc15c7e3e","source":{"kind":"arxiv","id":"0807.4832","version":1},"attestation_state":"computed","paper":{"title":"Concentration of the ratio between the geometric and arithmetic means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"J. M. Aldaz","submitted_at":"2008-07-30T10:36:44Z","abstract_excerpt":"We explore the concentration properties of the ratio between the geometric mean and the arithmetic mean, showing that for certain sequences of weights one does obtain concentration, around a value that depends on the sequence."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0807.4832","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.MG","submitted_at":"2008-07-30T10:36:44Z","cross_cats_sorted":["math.CA"],"title_canon_sha256":"3d3c4e66d2ef159340739de346a4db46b3eb508cb9353529b2a7bc6ec711e3c5","abstract_canon_sha256":"af2861b1c39d49af3be4ff0ae6d3b52f798d9e2a87fa1479364cc8d45feea575"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:39:08.311851Z","signature_b64":"unPafIAqLvNgeBT/Srzk095XEAHmYIHRUAS/xH1TY7kl/spakYgSvajMYfaRkFpgJsX+jEJkgL1YHPqSiKuSDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8fe312c9302e83d7d3ac8dc35aa0321557342400f6f7b1f52306179cc15c7e3e","last_reissued_at":"2026-05-18T04:39:08.311335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:39:08.311335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Concentration of the ratio between the geometric and arithmetic means","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.MG","authors_text":"J. M. Aldaz","submitted_at":"2008-07-30T10:36:44Z","abstract_excerpt":"We explore the concentration properties of the ratio between the geometric mean and the arithmetic mean, showing that for certain sequences of weights one does obtain concentration, around a value that depends on the sequence."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4832","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0807.4832","created_at":"2026-05-18T04:39:08.311403+00:00"},{"alias_kind":"arxiv_version","alias_value":"0807.4832v1","created_at":"2026-05-18T04:39:08.311403+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4832","created_at":"2026-05-18T04:39:08.311403+00:00"},{"alias_kind":"pith_short_12","alias_value":"R7RRFSJQF2B5","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"R7RRFSJQF2B5PU5M","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"R7RRFSJQ","created_at":"2026-05-18T12:25:58.018023+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/R7RRFSJQF2B5PU5MRXBVVIBSCV","json":"https://pith.science/pith/R7RRFSJQF2B5PU5MRXBVVIBSCV.json","graph_json":"https://pith.science/api/pith-number/R7RRFSJQF2B5PU5MRXBVVIBSCV/graph.json","events_json":"https://pith.science/api/pith-number/R7RRFSJQF2B5PU5MRXBVVIBSCV/events.json","paper":"https://pith.science/paper/R7RRFSJQ"},"agent_actions":{"view_html":"https://pith.science/pith/R7RRFSJQF2B5PU5MRXBVVIBSCV","download_json":"https://pith.science/pith/R7RRFSJQF2B5PU5MRXBVVIBSCV.json","view_paper":"https://pith.science/paper/R7RRFSJQ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0807.4832&json=true","fetch_graph":"https://pith.science/api/pith-number/R7RRFSJQF2B5PU5MRXBVVIBSCV/graph.json","fetch_events":"https://pith.science/api/pith-number/R7RRFSJQF2B5PU5MRXBVVIBSCV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/R7RRFSJQF2B5PU5MRXBVVIBSCV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/R7RRFSJQF2B5PU5MRXBVVIBSCV/action/storage_attestation","attest_author":"https://pith.science/pith/R7RRFSJQF2B5PU5MRXBVVIBSCV/action/author_attestation","sign_citation":"https://pith.science/pith/R7RRFSJQF2B5PU5MRXBVVIBSCV/action/citation_signature","submit_replication":"https://pith.science/pith/R7RRFSJQF2B5PU5MRXBVVIBSCV/action/replication_record"}},"created_at":"2026-05-18T04:39:08.311403+00:00","updated_at":"2026-05-18T04:39:08.311403+00:00"}